The Planck constant and its units
Abstract
We urge spectroscopists to use the units cycle s^{1} or radian s^{1} , with an appropriate prefix such as kilo as needed, when expressing the value of a transition frequency; the hertz (Hz) should be explicitly defined as being cycle s^{1}. Currently, in The International System of Units (SI), the unit of angular measure (cycle or radian) is omitted and transition frequencies simply have the unit s^{1} which is called the hertz. The use of the symbols ν (or f) and ω is supposed to carry the information as to which angular unit obtains. The omission of the unit of angular measure can lead to an error of 2π. In using the rules of quantity calculus to express the value of a transition frequency, and of the Planck constant, it is necessary to include the unit of angular measure. One result of doing this shows that h and ℏ each represent the value of the Planck constant, but with the units J s cycle^{1} and J s radian^{1} , respectively.
 Publication:

Journal of Quantitative Spectroscopy and Radiative Transfer
 Pub Date:
 November 2019
 DOI:
 10.1016/j.jqsrt.2019.106594
 Bibcode:
 2019JQSRT.23706594B
 Keywords:

 Transition frequencies;
 The Planck Constant;
 Angular measure;
 cycle/s;
 radian/s